Let $$\cos(\alpha+\beta)= -\frac{1}{10} \text{and} \sin (\alpha -\beta)= \frac{3}{8}$$, where $$0<\alpha<\frac{\pi}{3}$$ and $$0<\beta<\frac{\pi}{4}$$. If $$\tan 2\alpha = \frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})}, r,s\in N$$, then r + s is equal to __________.